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Number theory Difficulty 1.3 Junior Find the answer Canada

Which of the following integers is equal to a perfect square?

Pick one

Solution

Since $4 = 2^2$ , then $4^7 = (2^2)^7 = 2^{14} = (2^7)^2$ , which
means that $4^7$ is a perfect
square.

We can check, for example using a calculator, that the square root of
each of the other four choices is not an integer, and so each of these
four choices cannot be expressed as the square of an integer.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.